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On blow-up for the supercritical defocusing nonlinear wave equation
- 来源：
- 学校官网
- 收录时间：
- 2025-11-20 13:50:07
- 时间：
- 2025-11-16 15:00:00
- 地点：
- 腾讯会议
- 报告人：
- 韦东奕
- 学校：
- -/-
- 关键词：
- nonlinear wave equation, blow-up, supercritical, defocusing, relativistic Euler equations, self-similar solutions
- 简介：
- In this paper, we consider the defocusing nonlinear wave equation $-\partial_t^2u+\Delta u=|u|^{p-1}u$ in $\R\times \R^d$. Building on our work: Self-similar imploding solutions of the relativistic Euler equations, we prove that for $d=4, p\geq 29$ and $d\geq 5, p\geq 17$, there exists a smooth complex-valued solution that blows up in finite time.
- -/- 27
报告介绍：
In this paper, we consider the defocusing nonlinear wave equation $-\partial_t^2u+\Delta u=|u|^{p-1}u$ in $\R\times \R^d$. Building on our work: Self-similar imploding solutions of the relativistic Euler equations, we prove that for $d=4, p\geq 29$ and $d\geq 5, p\geq 17$, there exists a smooth complex-valued solution that blows up in finite time.
报告人介绍：
韦东奕，北京大学数学科学学院研究员，主要研究方向是偏微分方程的数学理论，在流体力学方程、非线性波动方程、奇点分析以及稳定性问题等方面取得了具有国际影响力的研究成果。世界闻名的布尔巴基讨论班组织专题讨论班，讨论他们在流动稳定性方面的成果。近期他和合作者通过发现相对论欧拉方程与波动方程的内在联系，构造了超临界非线性散焦波动方程的爆破解，成果发表在国际顶尖杂志Forum Pi上。
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